GATE ME 2021 Set 1 — Question 52
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Industrial Engineering → Operations Research → Queuing Models (M/M/1)
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Question
Consider a single machine workstation to which jobs arrive according to a Poisson distribution with a mean arrival rate of 12 jobs/hour. The process time of the workstation is exponentially distributed with a mean of 4 minutes. The expected number of jobs at the workstation at any given point of time is ________ (round off to the nearest integer).
Correct answer
4 to 4
Solution
This problem follows the queueing model.Given:
Arrival rate, jobs/hour
Mean service time, minutes hours hours
Service rate, jobs/hourUtilization factor (traffic intensity), The expected number of jobs at the workstation (in the system), , is given by:Rounding off to the nearest integer, the expected number of jobs is 4.
Arrival rate, jobs/hour
Mean service time, minutes hours hours
Service rate, jobs/hourUtilization factor (traffic intensity), The expected number of jobs at the workstation (in the system), , is given by:Rounding off to the nearest integer, the expected number of jobs is 4.
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